4MA0 Higher January 2013 Paper 4 Q23
23 f is a function such that \[\text{f}(x) = \frac{1}{x^2 + 1}\]
(a) Find \(\text{f}\left(\tfrac{1}{2}\right)\) (1)
g is a function such that \(\text{g}(x) = \sqrt{x - 1}\), \(x \geqslant 1\)
(b) Find \(\text{fg}(x)\)
Give your answer as simply as possible. (2)
Give your answer as simply as possible. (2)
| Scheme | Marks |
|---|---|
| \(\tfrac{4}{5}\) oe | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(\dfrac{1}{(\sqrt{x - 1})^2 + 1}\) or \(\dfrac{1}{x - 1 + 1}\) | M1 |
| \(\dfrac{1}{x}\) | A1 |
| (2) |
Notes
A1: Also accept \(x^{-1}\)